Arduino based incubator - hangs - SOLVED - power supply issues

So I had to increase the time interval each screen is displayed from 8 to 12 seconds

That's disturbing - could that be causing an issue with not resetting the watchdog timer soon enough as well? Also, what on earth is consuming that time?

On the topic of missing screens of LCD data, I'd be inclined to just flip to the next one every eight seconds, rather than using multiple measures such as LCDHUM2. I don't believe it's causing a problem, but it would make the code a little simpler.

Can you use softwareserial for the LCD and reserve the serial port for debug? Although it sounds like you're not going to be around to capture that data anyway. Somehow you need to be able to indicate where you were when it crashed. Is the watchdog masking your ability to tell?